{
  "id": "1303.0581",
  "version": "v1",
  "published": "2013-03-03T23:35:27.000Z",
  "updated": "2013-03-03T23:35:27.000Z",
  "title": "Abundant rich phase transitions in step skew products",
  "authors": [
    "L. J. Díaz",
    "K. Gelfert",
    "M. Rams"
  ],
  "comment": "5 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "We study phase transitions for the topological pressure of geometric potentials of transitive sets. The sets considered are partially hyperbolic having a step skew product dynamics over a horseshoe with one-dimensional fibers corresponding to the central direction. The sets are genuinely non-hyperbolic containing intermingled horseshoes of different hyperbolic behavior (contracting and expanding center). We prove that for every $k\\ge 1$ there is a diffeomorphism $F$ with a transitive set $\\Lambda$ as above such that the pressure map $P(t)=P(t\\, \\varphi)$ of the potential $\\varphi= -\\log \\,\\lVert dF|_{E^c}\\rVert$ ($E^c$ the central direction) defined on $\\Lambda$ has $k$ rich phase transitions. This means that there are parameters $t_\\ell$, $\\ell=1,...,k$, where $P(t)$ is not differentiable and this lack of differentiability is due to the coexistence of two equilibrium states of $t_\\ell\\,\\varphi$ with positive entropy and different Birkhoff averages. Each phase transition is associated to a gap in the central Lyapunov spectrum of $F$ on $\\Lambda$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-03-03T23:35:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D25",
      "37D35",
      "28D20",
      "28D99",
      "37D30",
      "37C29"
    ],
    "keywords": [
      "abundant rich phase transitions",
      "non-hyperbolic containing intermingled horseshoes",
      "step skew product dynamics",
      "central direction"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1088/0951-7715/27/9/2255",
      "journal": "Nonlinearity",
      "year": 2014,
      "month": "Sep",
      "volume": 27,
      "number": 9,
      "pages": 2255
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014Nonli..27.2255D"
    }
  }
}